SOLUTION: The length of a rectangle is 10cm more than its width if the area is 80cm^2 calculate it's perimeter

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Question 918902: The length of a rectangle is 10cm more than its width if the area is 80cm^2 calculate it's perimeter
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

     .

A = (w+10)w = 80cm^2

w^2 + 10w - 80 = 0 

(Tossing out the negative solution for unit measure)

w = 5.247 (rounded) and L = 15.247 

P = 2(20.247) cm = 40.247

 


 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B10x%2B-80+=+0) has the following solutons:

  

  x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

  

  For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

  

  First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2810%29%5E2-4%2A1%2A-80=420.

  

  Discriminant d=420 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+420+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+420+%29%29%2F2%5C1+=+5.2469507659596

    x%5B2%5D+=+%28-%2810%29-sqrt%28+420+%29%29%2F2%5C1+=+-15.2469507659596

    

    Quadratic expression 1x%5E2%2B10x%2B-80 can be factored:

  1x%5E2%2B10x%2B-80+=+1%28x-5.2469507659596%29%2A%28x--15.2469507659596%29

  Again, the answer is: 5.2469507659596, -15.2469507659596.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B-80+%29